Question

(a) Calculate the molarity of a solution that contains 0.175 mol \(Z \mathrm{nCl}_{2}\) in exactly 150 \(\mathrm{mL}\) of solution. (b) How many moles of protons are present in 35.0 \(\mathrm{mL}\) of a 4.50 \(\mathrm{M}\) solution of nitric acid? (c) How many milliliters of a 6.00\(M\) NaOH solution are needed to provide 0.350 mol of \(\mathrm{NaOH}\) ?

Short answer

The short answer to this question is as follows: (a) The molarity of the ZnCl₂ solution is \(M = \frac{0.175\,\text{mol}}{0.150\,\text{L}} = 1.17\,\text{M}\). (b) The number of moles of protons in the nitric acid solution is \(\text{moles of protons} = 4.50\,\text{M} \times 0.0350\,\text{L} = 0.1575\,\text{mol}\) of H⁺ ions. (c) The volume of the 6.00 M NaOH solution needed to provide 0.350 mol of NaOH is \(V = \frac{0.350\,\text{mol}}{6.00\,\text{M}} = 0.0583\,\text{L}\), which is equivalent to \(58.3\,\text{mL}\) of NaOH solution.

Step-by-step solution

(Part a: Calculate the molarity of the ZnCl₂ solution)

To calculate the molarity of the ZnCl₂ solution, we'll use the formula \(M = \frac{n}{V}\), where \(n = 0.175\) mol ZnCl₂ and \(V = 150\) mL, which needs to be converted to liters. Divide the volume in milliliters by 1000 to get the volume in liters: \(V = \frac{150}{1000} = 0.150 L\). Plugging in the values, we have \(M = \frac{0.175\,\text{mol}}{0.150\,\text{L}}\).

(Part b: Calculate the number of moles of protons in the nitric acid solution)

The nitric acid solution has a molarity of 4.50 M and we have 35.0 mL of it. First, convert the volume to liters: \(V = \frac{35.0}{1000} = 0.0350\,\text{L}\). Since nitric acid (HNO₃) donates one proton (H⁺) per molecule, we can use the molarity of the solution to find the number of moles of protons. The formula is: \(\text{moles of protons} = M \times V\). Plug in the values: \(\text{moles of protons} = 4.50\,\text{M} \times 0.0350\,\text{L}\).

(Part c: Calculate the volume of NaOH solution needed to provide 0.350 mol of NaOH)

We have a 6.00 M NaOH solution and need 0.350 mol of NaOH. Use the formula for molarity: \(M = \frac{n}{V}\). Rearrange it to find V: \(V = \frac{n}{M}\). Plug in the values: \(V = \frac{0.350\,\text{mol}}{6.00\,\text{M}}\). The volume will be in liters. To convert it to milliliters, multiply the result by 1000.

Key concepts

Solution Concentration

Understanding solution concentration is fundamental when working with chemical solutions. It refers to the amount of a substance, known as the solute, that is dissolved in a certain volume of solvent. The concentration can be expressed in various ways, including molarity, which is one of the most common methods used in chemistry.

When we talk about molarity, we're referring to the number of moles of solute per liter of solution. This is depicted by the symbol M and calculated using the formula: \( M = \frac{n}{V} \), where \( n \) represents the number of moles and \( V \) is the volume of the solution in liters.

For example, to understand the concentration of a solution in a given exercise, you must first determine the amount of the solute (in moles) and the volume of the total solution (in liters). With this information, you can easily calculate its molarity, providing insight into how concentrated the solution is. This concept is important not only for solving problems but also for preparing solutions correctly in practical laboratory settings.

Moles and Molarity

Delving into the concept of moles and molarity, we need to grasp that a mole is a unit of measurement used in chemistry to express amounts of a chemical substance. One mole corresponds to Avogadro's number (\(6.022 \times 10^{23} \) entities) of molecules or atoms, depending on the substance.

When you relate moles to molarity, you connect the amount of substance to the volume of the solution in which it's dissolved. Molarity (\(M\)) expresses the moles of solute (\(n\)) per liter of solution (\(V\)). This relationship is crucial for calculations in chemistry; for instance, if you're tasked with identifying the number of moles of protons in a solution based on its molarity, the process involves simply multiplying the molarity by the volume (in liters) of the solution.

For practical purposes, remember that each substance will contribute a different number of moles of particles such as protons, based on its dissociation in solution. Understanding this concept is essential for stoichiometric calculations and predicting the outcomes of chemical reactions. The step-by-step example from the exercise demonstrates how molarity helps calculate the amount of substance present in or needed to prepare a specific volume of solution.

Volume Conversion

When dealing with solutions, volume conversion becomes a necessary skill, as different units are often used interchangeably. The most common conversion you'll encounter is between milliliters (mL) and liters (L), with 1 liter equal to 1000 milliliters. Therefore, to convert milliliters to liters, you divide the number of milliliters by 1000.

Keeping this conversion in mind is crucial in chemistry, as molarity calculations require the volume to be in liters. If you come across a problem where the volume is given in milliliters, just remember to divide by 1000 to get the equivalent volume in liters, allowing you to continue with your molarity calculation. For instance, in the provided exercise, after finding the molarity or moles, you might need to report your final answer in milliliters; simply multiply the volume in liters by 1000 to convert it back.

Understanding volume conversion is not only helpful for solving textbook problems but also invaluable in real-life scenarios, such as scaling up reactions for industrial applications or diluting solutions to a desired concentration in the lab.